must be converted into tonnes
asked Aug 12 in Geometry Answers by Rafsan

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A box shaped vessel 20m x 6m x 2.5m floats at a draft of 1.5m in water of density 1013 kg per cu.m. Find the displacement in tonnes, and the height of the centre of buoyancy above the keel.

Displacement is the weight of water displaced.

Volume of water displaced is V = 20 * 6 * 1.5 = 180 m^3

Density of the water is 1013 kg/m^3

Weight of displaced water is 180 * 1013 = 182,340 kg

Displacement of ship is 182.34 tonnes

Centre of buoyancy is centre of gravity of the displaced water.

Since the displaced water has the shape/volume of a cuboid, then COG is half the draft = 0.75 m

Taking the keel to be the bottommost part of the box,

Height of the centre of buoyancy above the keel is 0.75 m

answered Aug 12 by Fermat Level 11 User (76,040 points)

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